Minimal Group Determinants For Dicyclic Groups

TL;DR

This paper calculates the smallest non-trivial integer group determinant for dicyclic groups of order 4n with odd n and explores the entire set of such determinants for groups of order 4p.

Contribution

It provides the first explicit determination of minimal integer group determinants for dicyclic groups of specific orders and characterizes their full set.

Findings

Minimal non-trivial integer group determinant for dicyclic groups of order 4n with odd n is determined.

Complete set of integer group determinants for dicyclic groups of order 4p is characterized.

Results extend understanding of group determinants for non-abelian groups.

Abstract

We determine the minimal non-trivial integer group determinant for the dicyclic group of order $4n$ when $n$ is odd. We also discuss the set of all integer group determinants for the dicyclic groups of order $4p$.